Alaska is about 5,611 times bigger than Cayman Islands.

Cayman Islands is approximately 264 sq km, while Alaska is approximately 1,481,348 sq km, making Alaska 561,017% larger than Cayman Islands. Meanwhile, the population of Cayman Islands is ~64,309 people (645,922 more people live in Alaska).
Tip: This to-scale comparison of Cayman Islands vs. Alaska uses the Mercator projection, which distorts the size of regions near the poles.